GPDs are Fourier transorm along the light-cone of non-local matrix elements between two different hadronic states. You are probably aware of that. More precisely, if you consider the vector case you find the two GPDs [tex]H[/tex] and [tex]E[/tex] :
[tex]\int\frac{\text{d}\lambda}{2\pi}e^{-\imath\lambda x}\langle P_2|\bar{\Psi}^q(-\frac{\lambda n}{2})\gamma^+\Psi^q(\frac{\lambda n}{2})| P_1 \rangle=\bar{U}(P_2)\left[H^q(x,\xi,t)\gamma^+
+E^q(x,\xi,t)\frac{\imath\sigma^{+i}q_i}{2M}\right] U(P_1)[/tex]
and similarly if you replace [tex]\gamma^+\rightarrow\gamma^+\gamma_5[/tex] you'll get the axial-vector GPDs [tex]\tilde{H}[/tex] and [tex]\tilde{E}[/tex], and if you replace [tex]\gamma^+\rightarrow\sigma^{+\perp}\gamma_5[/tex] you would get four more transversity GPDs which are chiral odd and usually suppressed by at least one power of [tex]Q[/tex].

The link to PDFs is quite simple. Take the limit [tex]\xi\rightarrow 0[/tex] and [tex]t\rightarrow 0[/tex]. For instance [tex]H^{q}(x,0,0)=q(x)[/tex]. If you consider [tex]\tilde{H}[/tex] instead you'll get to helicity dependent PDFs.

The link to FFs is also rather simple. Take the first Mellin moment with respect to [tex]x[/tex] :
[tex]\int_{-1}^{1}\text{d}x\, H^q(x,\xi,t)=F^{\:q}_1(t)[/tex] (Dirac FF). And similarly with [tex]E\leftrightarrow F_2[/tex] (Pauli FF), [tex]\tilde{H}\leftrightarrow g_{A}[/tex] and [tex]\tilde{E}\leftrightarrow g_{P}[/tex].

It is quite annoying that I cannot check my formulae as I type them...